Optimal decay for a wave-heat system with Coleman-Gurtin thermal law
arXiv:2101.11397 · doi:10.1016/j.jmaa.2022.126706
Abstract
We study the long-term behaviour of solutions to a one-dimensional coupled wave-heat system with Coleman-Gurtin thermal law. Our approach is based on the asymptotic theory of -semigroups and recent results developed for coupled control systems. As our main results, we represent the system as a feedback interconnection between the wave part and the Coleman-Gurtin part and we show that the associated semigroup in the history framework of Dafermos is polynomially stable with optimal decay rate as . In particular, we obtain a sharp estimate for the rate of energy decay of classical solutions to the problem.
Accepted for publication in Journal of Mathematical Analysis and Applications